# simplicial approximation theorem

Let $f:|K|\to|L|$ be continuous function, where $|K|$ and $|L|$ are polyhedra having triangulations $K$ and $L$, respectively.

Then there is a barycentric subdivision $K^{(s)}$ of $K$ and a continuous function $g:|K|\to|L|$ such that $g$ is a simplicial map from $K^{(s)}$ to $|L|$ and $g$ is homotopic to $f$.

The theorem is due to J.W. Alexander.

## References

• 1 J.W. Alexander , Combinatorial analysis situs, Trans. Amer. Math. Soc. 28, 301-329, (1926)
Title simplicial approximation theorem SimplicialApproximationTheorem 2013-03-22 16:54:29 2013-03-22 16:54:29 Mathprof (13753) Mathprof (13753) 5 Mathprof (13753) Theorem msc 55U10